Explore BrainMass
Share

Explore BrainMass

    Isomorphic group

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Consider the cartesian product H=Z_2 X Z_n (as a set).Define a binary operation on H to be (i,j)*(k,l)=(i+k,(-1)^k *j+l), where i,j,k and l are vectors.

    Show that H is a group under this operation, determine its order.

    Let G = < a,b|a^n=1, b^2=1, abab^-1=1 >
    Show that |G|<=2n.

    Show that H is isomorphic to G.

    See attached file

    © BrainMass Inc. brainmass.com October 9, 2019, 10:57 pm ad1c9bdddf
    https://brainmass.com/math/discrete-math/isomorphic-group-238580

    Attachments

    Solution Summary

    This provides an example of proving something is a group and that it is isomorphic.

    $2.19